Method for NMR spectroscopy with sustained induction decays of long-lived coherences

ABSTRACT

A method for nuclear magnetic resonance (NMR) spectroscopy of a sample involves excitation of long lived coherences (LLC) between the singlet state S 0  and the central triplet state T 0  of nuclei of the sample by initiating irradiation of the sample with an rf-field with carrier frequency ω rf ; sustaining of the LLC by maintaining the rf-irradiation during an interval τ 2 ; converting the LLC temporarily into observable magnetization by interrupting the rf-irradiation during an observation interval τ 3 ; detecting NMR-signals during the observation interval τ 3  and reconversion of the observable magnetization back into LLC after the observation interval τ 3 . These steps are repeated n times, wherein n is a positive integer. The method allows ultra high-resolution spectra of long-lived coherences to be obtained.

This application claims Paris convention priority of EP 11 165 564.3filed May 10, 2011, the entire disclosure of which is herebyincorporated by reference.

BACKGROUND OF THE INVENTION

The invention concerns a method for nuclear magnetic resonance (NMR)spectroscopy of a sample comprising the following steps:

-   (a) excitation of long lived coherences (LLC) between the singlet    state S₀ and the central triplet state T₀ of nuclei of the sample by    initiating irradiation of the sample with an rf-field with a carrier    frequency;-   (b) sustaining of the LLC by maintaining the rf-irradiation during    an interval τ₂;-   (c) converting the LLC temporarily into observable magnetisation by    interrupting the rf-irradiation during an observation interval τ₃;-   (d) detecting NMR-signals during the observation interval τ₃.

Most nuclear magnetic resonance (NMR) methods employ Fouriertransformations of free induction decays (FID's).¹ Though widely used,this approach suffers from homogeneous decay and imperfect homogeneityof a static magnetic field, so that it is challenging to achieveline-widths below 1 Hz.² Sophisticated NMR pulse sequences have beendeveloped to achieve reasonable line-widths (1<Δν<50 Hz) in moderatelyinhomogeneous fields, exploiting cross relaxation effects³, observationin the earth's magnetic field⁴, or a spatial correlation between thestatic and radio-frequency (rf) field profiles⁵. By combining refocusingand coherence transfer through couplings, one can obtain acceptableline-widths (1<Δν<50 Hz) even in very inhomogeneous fields (Δν>2 kHz).⁶In systems with two scalar-coupled homonuclear spins I=½ and S=½, onecan excite long-lived coherences (LLC's) that can have very longlife-times T_(LLC) and hence very narrow line-widthsΔν_(LLC)=1/(π/T_(LLC)).⁷⁻⁹ Their precession frequency is independent ofoffset (and hence of chemical shifts and inhomogeneous broadening) andis only determined by the sum of scalar and residual dipolar couplings(T_(IS)=J_(IS)+2D_(IS)). So far, LLC's have only been observedindirectly in the manner of two-dimensional (2D) spectroscopy, i.e.point by point, either in combination with field cycling⁷ or in highfield.⁸⁻⁹

Principles

Long-lived coherences (LLC's) constitute a class of zero-quantumcoherences that can be excited by extremely low frequency fields (ELF's)in a vanishing static field.⁷ LLC's can also be excited in high fieldsby creating a state where the coherences I_(y) and −S_(y) have oppositephases, so that they can be locked by a continuous ‘sustaining’ rffield⁸⁻⁹. This rf field in effect suppresses the chemical shifts, thusrendering the spins magnetically equivalent, so that their eigenstatescan be classified according to ‘symmetrical’ and ‘antisymmetrical’irreducible representations of the spin permutation group. LLC's spanzero-quantum transitions between states of different symmetry. Theiroscillatory decays can be subjected to a Fourier transformation,yielding doublets that are reminiscent of ‘J-spectroscopy’¹¹⁻¹³. Thelife-times T_(LLC) of LLC's can be a factor κ longer than the transverserelaxation times T₂=T_(SQC) of ordinary single-quantum coherences(T_(LLC)=κT₂), so that the line-widths Δν_(LLC)=1/(πT_(LLC)) can benarrower by a factor Δν_(LLC)/Δν_(SQC)=1/κ. Depending on the role ofextraneous relaxation mechanisms⁹, one can expect κ≦3 in small moleculesin the extreme narrowing limit, and κ≦9 in the slow¹⁴ motion limittypical of large molecules. In practice, we have observed 2.5<κ<4.3 overa range of correlation times.¹⁵

Generally speaking, LLC's should not be confused with long-lived states(LLS's), also known as singlet states (SS) if there are only two spinsin the system. LLS's refer to populations of antisymmetric singletstates¹⁶⁻²⁸. LLS's have life-times that can be much longer than LLC's(T_(LLS)>>T_(LLC)), but do not have any oscillatory character, andcannot give rise to J-spectra in the manner of LLC's. Both LLS's andLLC's can be temporarily converted into observable magnetisation (videinfra). This is of particular interest when the initial polarization isenhanced by ‘dissolution’ DNP^(10,21).

If the oscillatory decays of LLC's are observed point-by-point in themanner of two-dimensional (2D) spectroscopy, they cannot be enhanced(‘hyperpolarized’) by ‘dissolution’ DNP. Recently, several 2Dexperiments have been successfully converted into ‘ultra-fast’ versionsthat can be combined with ‘dissolution’ DNP.²²⁻²³ However, thecontinuous rf field, which is preferably used to sustain LLC's is notcompatible with current ‘ultra-fast’ schemes.

It is an object of the present invention to propose a method that allowsobtaining ultra high-resolution spectra of long-lived coherences withenhanced resolution.

SUMMARY OF THE INVENTION

This object is achieved by:

(e) reconverting the observable magnetisation back into LLC after theobservation interval τ₃; and repeating steps (b)-(e) n times, with n isa positive integer.

The irradiation of step (b) is resumed and the loop is repeated n times,where the integer n can be preferably 100 or more. It is clear for onewho is skilled in the art that in the final repetition step (e) can beomitted without leaving the scope of the invention.

A long lived coherence (LLC) is a coherent superposition between thesinglet and the central triplet state of two nuclei of the same kind.Long-lived coherences (LLC's) constitute a class of zero-quantumcoherences. The excitation of LLC is carried out in a magnetic field, inparticular in the magnetic field of the NMR magnet. Pairs of nuclei arechosen from the sample. The excitation of LLC comprises a transformationof an initial spin distribution (I_(z)+S_(z)) into (I_(x)−S_(x)) or(I_(y)−S_(y)) or (2I_(y)S_(z)−2I_(z)S_(y)) or (2I_(x)S_(z)-2I_(z)S_(x))respectively just before the rf-field is applied, i.e. the initial spindistribution (I_(z)+_(Z)) is flipped to the transverse plane (observablemagnetisation). The excitation can be achieved by various preparations,e.g., by applying a non-selective (π/2)_(x) or (π/2)_(y)-pulse or byapplying a semi-selective π-pulse that affects only the multiplet ofeither spin I or spin S, followed by a non-selective (π/2)_(x) or(π/2)_(y)-pulse, or by using an echo sequence with a band-selectiverefocusing pulse, or by using a long lived state filter. Otherpreparations are also possible. (I_(x)−S_(x)) or (I_(y)−S_(y)) or(2I_(y)S_(z)−2I_(z)S_(y)) or (2I_(x)S_(z)-2I_(z)S_(x)) is thentransformed into LLC by initiating irradiation of the rf-field. The LLCare sustained as long as rf-irradiation is applied.

When the rf-irradiation is interrupted, the LLC is no longer sustained,but converted into observable magnetisation, whereby “observablemagnetisation” means magnetisation which is detectable by MRmeasurements (transverse magnetisation, in particular single quantumcoherences (I_(x)−S_(x))). When the sustaining rf field is switched onagain, the remaining observable magnetization (differences (I_(x)−S_(x))or (I_(y)−S_(y)) or (2I_(y)S_(z)−2I_(z)S_(y)) or(2I_(x)S_(z)−2I_(z)S_(x))) are reconverted into LLC's, while the sum(I_(x)+S_(x)) or (I_(x)+S_(y)) is spin-locked and decays, and the sum2I_(y)S_(z)+2I_(z)S_(y) is dephased under the effect of the rf fieldinhomogeneity. The repetition of sustaining of the rf-field,interrupting the rf-field and detecting NMR-signals during theobservation interval results in partial decay of the LLC.

The RF irradiation can consist of a composite pulse scheme comprising amanifold of pulses and phases. Nevertheless the rf-irradiation ispreferably carried out along an x-axis, if the LLC contains(I_(x)−S_(x)) terms and along the y-axis if the LLC contains(I_(y)−S_(y)) terms, whereby the x-axis and the y-axis of the rotatingreference frame are both perpendicular to the z-direction of the staticfield, in which the experiment is carried out.

During the irradiation intervals τ₂, the coherence LLC evolves under theeffect of the total coupling 2T_(IS)=2J_(IS)+4D_(IS) and decays with therelaxation rate R_(LLC)=1/T_(LLC). During each observation interval(observation window τ₃), the system evolves under the chemical shiftsand again under the total coupling constant T_(IS), albeit reduced by afactor 2, and decays with the single-quantum relaxation rate R₂=1/T₂.

The duration τ3 of the observation interval can be equal for eachrepetition. Yet, it is also possible to choose non-constant durationsfor the observation interval (i.e. τ3 may be different in differentrepetitions) to achieve sparse sampling.

This invention shows that a signal comprising a larger number n of datapoints can be obtained in a single scan. With the inventive method,long-lived coherences (LLC's) in homonuclear pairs of chemicallyinequivalent spins can be excited and sustained during protractedradio-frequency irradiation periods that alternate with brief windowsfor signal observation (observation interval). Fourier transformation ofthe sustained induction decays recorded in a single scan yields NMRspectra with line-widths in the range 10<Δν<100 mHz, even in moderatelyinhomogeneous magnetic fields. If the windows for signal observationhave a duration that is negligible compared to the protractedirradiation periods, the line-widths Δν approach the limitingline-widths Δν_(LLC). Even in poorly shimmed magnets where theinhomogeneous line width is Δν*>20 (protons) Hz, the inventive methodcan provide line-widths as narrow as Δν_(LLC)=14 mHz. The resultingdoublets, which are reminiscent of 1-spectra, allow one to determine thesum of scalar and residual dipolar interactions in partly orientedmedia.

In a variant of the inventive method, the LLC are excited bytransforming an initial spin polarization, (I_(z)+S_(z)), in particularthe thermal equilibrium Boltzmann distribution, of the spin polarization(I_(z)+S_(z)) into single quantum coherences (I_(x)−S_(x)) or(I_(y)−S_(y)) or (2I_(y)S_(z)−2I_(z)S_(y)) or (2I_(z)S_(z)−2I_(z)S_(z))prior to initiating irradiation of the sample with the rf-field.

Alternatively the sample is hyperpolarized, in particular by usingdynamic nuclear polarization, thereby enhancing the spin polarization(I_(z)+S_(Z)) and the LLC that are subsequently excited by transformingthe enhanced spin polarization (I_(z)+S_(z)) into enhanced singlequantum coherences (I_(x)−S_(x)) or (I_(y)−S_(y)) or(2I_(y)S_(z)−2I_(z)S_(y)) or (2I_(z)S_(x)−2I_(z)S_(x)), prior toinitiating irradiation of the sample with the rf-field. Thereby thesignal to noise ratio can be improved.

In a preferred variant the carrier frequency is ω_(rf)=(Ω_(I)−Ω_(S))/2,with Ω_(I) chemical shift of nuclei of the sample with spin I, and Ω_(S)chemical shift of nuclei of the sample with spin S.

If the carrier frequency is chosen half-way between the two chemicalshifts σ=−I_(y)−S_(y) is entirely transformed into σ=I_(x)−S_(x) duringthe preparation.

The rf-field is a preferably a continuous wave-rf-field. A continuouswave rf-field constitutes the simplest way to sustain the LLC.

In a special variant the rf-field is modulated in amplitude.

Alternatively or additionally the rf-field is modulated in phase.

It is preferred that that the amplitude of the rf-field is larger thanthe offset in, |Ω_(I)−Ω_(S)|/2.

In a highly preferred variant a refocusing pulse is applied in themiddle of the observation interval τ₃. Contributions to the LLC from(I_(x)+S_(x)), (I_(y)+S_(y)) and (2I_(x)S_(z)+2I_(z)S_(x)) and(2I_(y)S_(z)+2I_(z)S_(y)), can be suppressed by using a π pulse in themiddle of each window to refocus the chemical shifts. This enables amore accurate measurement of the scalar coupling J_(IS) and the totalcoupling T_(IS)=J_(IS)+2D_(IS) even for long observation intervals τ3,in particular 100 μs<τ₃<2 ms. Long observation intervals allow one toaverage over a larger number of data points in each window, resulting inimproved signal-to-noise ratios. The detection of NMR-signals ispreferably carried out during the first half τ₃/2 of the observationinterval τ3. But it is also possible to detected NMR-signals in thesecond half τ₃/2 of the observation interval.

In a preferred variant the NMR spectroscopy measurement is carried outin a single experiment. A “single experiment” comprises one singlepreparation, i.e. only one single excitation of long lived coherences byapplying rf-pulses.

Further advantages can be extracted from the description and theenclosed drawings. The features mentioned above and below can be used inaccordance with the invention either individually or collectively in anycombination. The embodiments mentioned are not to be understood asexhaustive enumeration but rather have exemplary character for thedescription of the invention.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 shows pulse sequences for exciting and sustaining LLC's accordingto the invention. A complete pulse sequence comprises a preparationsequence and a sustaining/detection sequence. Each one of the foursuggested preparation sequences A1-A4 allows one to create a densityoperator σ=I_(x)−S_(x). Either of the two sustaining/detection sequencesB1 and B2 can be used to sustain the LLC's by CW irradiation and toacquire signals in the windows τ₃ or τ₃/2. The sustaining-acquisitionblocks are repeated n times;

FIG. 2 shows examples of FID's and SID's recorded ‘on the fly’ by usingthe inventive method, together with their Fourier transforms:

-   -   a, Real part of a conventional ‘free induction decay’ (FID) due        to single-quantum coherences (SQC's) of the two protons of        2,3-dibromothiophene in a 20 mM isotropic solution in DMSO-d₆        with 30 mM ascorbic acid, measured at 11.7 T (500 MHz for        protons) and 296 K;    -   b, Conventional Fourier transform of the FID in (a), showing a        doublet with average line widths <Δν>≈1.5 Hz and a splitting        J_(IS)≈5.8 Hz;    -   c, Real part of the echo amplitude of 2,3-dibromothiophene in a        20 mM isotropic solution in DMSO-d₆ with 30 mM ascorbic acid        (note that the time scale was expanded by a factor 18 with        respect to (a)) which was measured with conventional J-resolved        ¹H spectroscopy²⁹;    -   d, Positive projection of the 2-dimensional Fourier transform,        showing a doublet with line widths <Δν>≈70 mHz and a splitting        J_(IS)≈5.77 Hz;    -   e, Real part of the ‘sustained induction decay’ (SID) of the two        protons of 2,3-dibromothiophene in a 20 mM isotropic solution in        DMSO-d₆ with 30 mM ascorbic acid acquired ‘on the fly’ in a        single scan according to the present invention (note that the        time scale was expanded by a factor 100 with respect to (a)),        arising from an LLC excited in the same sample with sequence A3        of FIG. 1, sustained and observed with sequence B2, The        parameters were τ₃/2=100 μs, Δt=τ₂+τ₃=50 ms, rf amplitude of the        CW sustaining field γB₁/(2π)=4.5 kHz, offsets        Ω1/(2π)=−Ω_(S)/(2π)=145 Hz, the rf carrier being set half-way        between the two chemical shifts;    -   f, Spectrum obtained by a real Fourier transformation of the SID        of (e), showing a doublet with line widths <Δν>≈16.4 mHz and a        splitting 2J_(IS)≈11.5286 Hz. If undesirable spin-locked        I_(x)+S_(X) terms had not been suppressed, they would give rise        to peak at ν=0. The narrowest line-widths <Δν>=14 mHz (not        shown) were observed with scheme B1, τ₃=30 μs and Δt=τ₂+τ₃=50        ms;    -   g, Zoom of (d), with apparent scalar coupling constant J_(IS)        ^(app)=5764.3±0.2 mHz and <Δν>=16.4±0.1 mHz;    -   h, Zoom similar to (g) of an ‘on the fly’ LLC spectrum of the        two diastereotopic protons of glycine in L-Ala-Gly, with J_(IS)        ^(app)=17236.5±0.2 mHz and <Δν>=115.0±0.7 mHz;

FIG. 3 shows average life-times, apparent scalar couplings, andsignal-to-noise ratios.

-   -   a, Average life-times <T>=1/<R> (see Eq. (4)) in the same sample        of 2,3-dibromothiophene as in FIG. 2, measured as a function of        the duration of the observation windows τ₃ in scheme B1 without        refocusing pulses (•) and 2 τ₄ (2 τ₄=τ₃ in case the duration of        the refocussing pulse is neglected) in scheme B2 using π        refocusing pulses (∘), averaging signals sampled at a rate of        500 kHz in each interval, and adapting τ₂ to keep a constant        dwell time Δt=50 ms. The lines are drawn to guide the eye.    -   b, Apparent scalar coupling constant J_(IS) ^(app) in        2,3-dibromothiophene observed as a function of the duration of        τ₃ in scheme B1 (•) or in scheme B2 (∘) with a constant dwell        time Δt=50 ms.    -   c, Signal-to-noise ratio (S/N) for the same sample of        2,3-dibromothiophene determined with scheme B2 with 100 μs<τ₃<2        ms. The black line shows a fit to the function S/N˜τ₃ ^(1/2);

FIG. 4 shows a comparison of NMR spectra in a homogeneous and aninhomogeneous magnetic field.

-   -   a, Conventional (single-quantum) NMR spectra of the same sample        of 2,3-dibromothiophene as in FIG. 2, obtained by Fourier        transformation of an FID measured at 11.7 T (500 MHz for        protons), with the magnet shimmed to yield a line-width Δν*˜1.2        Hz and deliberately de-shimmed to yield a line-width Δν*˜20 Hz.    -   b, LLC spectra observed ‘on the fly’ of a sample of        2,3-dibromothiophene in a homogeneous (<Δν_(LLC)>=17.5±0.2 mHz        and J_(IS) ^(app)=5.741 Hz±0.1 mHz) and inhomogeneous field        (<Δν_(LLC)>=22.8±0.4 mHz and J_(IS) ^(app)=5.744 Hz±0.2 mHz). In        a poorly shimmed magnetic field, some broadening (+5.3 mHz) and        a slight error in J_(IS) ^(app) (+3 mHz) are thus observed. The        areas of the peaks are identical. The LLC's were excited with        sequence A3 and sustained and observed with sequence B2 of FIG.        1 with the following parameters: τ₄4=500 μs, Δt=τ₂+τ₃=50 ms, rf        amplitude of CW sustaining field γB1/(2π)=4.5 kHz;

FIG. 5 shows ‘on the fly’ LLC's according to the invention in a weaklyoriented medium. The LLC spectra of 3-bromothiophene-2-carboxylic acidin a (1:1) D₂O/DMSO-d₆ with and without addition of a very small amount(0.25%) of C₅E₁₂ were observed ‘on the fly’ at B₀=11.7 T (500 MHz forprotons) and T=300 K. The isotropic solution shows J_(IS)^(app)=5252.0±0.2 mHz and <Δν>≈18.5 mHz whereas the weakly alignedmedium gives T_(IS) ^(app)=J_(IS) ^(app)+2D_(IS) ^(app)=5241.3±0.2 mHzand <Δν>≈40.0 mHz, hence 2D_(IS) ^(app)=−10.7±0.4 mHz. The LLC's wereexcited with sequence A3 and sustained and observed with sequence B2 ofFIG. 1 with the following parameters: τ₃/2=500 μs, Δt=τ₂+τ₃=50 ms, rfamplitude of CW sustaining field γB₁/(2π)=4.5 kHz;

FIG. 6 shows hyperpolarized ‘on the fly’ LLC spectra of3-Bromothiophene-2-carboxylic acid, showing a 300-fold enhancement ofthe signal intensity.

-   -   a, The sample consisted of 20 μL of a 50 mM solution of        3-bromothiophene-2-carboxylic acid in a 3:2 DMSO-d₆/D₂O (v/v)        mixture, doped with 30 mM TEMPO, rapidly frozen, immersed in a        field of 3.35 T, hyperpolarized by 30 mW microwave irradiation        at 93.89 GHz at 1.2 K during 300 s, and dissolved with 3 mL of        preheated D₂O to a final concentration of 250 vLIVI        3-bromothiophene-2-carboxylic acid. The hyperpolarized sample        was rapidly transferred to B₀=11.7 T (500 MHz for protons) at        T=296 K, and the LLC was then excited with uence A3, sustained        and observed with sequence B2 of FIG. 1 with the following        parameters: τ₃/2=100 μs, Δt=τ₂+τ₃=50 ms, rf amplitude of CW        sustaining field γB₁/(2π)=4.5 kHz, offsets        Ω₁/(2π)=−Ω_(S)/(2π)=103 Hz, the rf carrier being set half-way        between the two chemical shifts.    -   b, Thermal equilibrium signal (i.e., without DNP) of the same        sample measured with the same parameters, but with 256 scans and        multiplied by a factor 10.

DESCRIPTION OF THE PREFERRED EMBODIMENT

In an experiment according to the invention, the signals are observedduring brief interruptions (observation interval τ₃) of a sustaining rffield (scheme B1 in FIG. 1). This leads to a temporary conversion ofLLC's into observable magnetization, e.g. I_(x)−S_(x). In the simplestversion of the inventive method, the observation intervals τ₃ are keptbelow 0.1 ms, so that the evolution of I_(x)−S_(x) under chemicalshifts, couplings and transverse relaxation can be neglected (FIG. 1B1). In a more sophisticated variant of the inventive method, thesensitivity can be improved by increasing the duration of theobservation intervals τ₃ beyond 0.1 ms, and by inserting π refocusingpulses in the centre of the observation intervals τ₃ (one refocusingpulse in each observation interval τ₃) to refocus chemical shifts(scheme B2 in FIG. 1).

In the example shown in FIG. 1 the initial populations, described by thedensity operator σ=I_(z)+S_(z) (which may be enhanced by DNP), istransformed into σ=I_(x)−S_(x). Scheme A1 of FIG. 1 starts with anon-selective (π/2)_(x) pulse to excite the state σ=−I_(y)−S_(y)followed by a delay τ₁=1/(2|ΔΩ_(IS)|), where ΔΩ_(IS)=Ω_(I)−Ω_(S). Sincethe rf carrier frequency is normally positioned half-way between the twochemical shifts at ω_(rf)=(Ω₁+Ω_(S))/2, σ=−I_(y)−S_(y) is transformedinto σ=I_(x)−S_(x) during the delay τ₁. The precession under J_(IS) inthe interval τ₁ can usually be neglected in weakly coupled systems where2πJ_(IS)<<ΔΩ_(IS).

In scheme A2, a semi-selective IC pulse applied to either spins I or Sto invert the populations across either of the two doublets isimmediately followed by a non-selective (π/2)_(y) pulse to exciteσ=I_(x)−S_(x).⁸⁻⁹ In aqueous solutions, it may be necessary to suppressthe intense HDO peak.

Scheme A3 uses an echo sequence (π/2)_(x)−τ−(π)_(x) ^((I,S))−τ− with aband-selective refocusing pulse that acts on spins I and S but is tooweak to refocus the solvent resonance. The two pulsed field gradients(PFG's) G₁ lead to dephasing of all magnetization components withoffsets that lie outside the range of the band-selective refocusingpulse. Like in scheme A1, σ=I_(x)−S_(x) is created after a delay, inscheme A3 the delay is 2τ+τ₁=2τ+1/(2|ΔΩ_(IS)|).

Finally, scheme A4 uses a ‘long-lived state filter’ as explainedelsewhere¹⁵. The latter two schemes also have the advantage of avoidingpossible radiation damping induced by large HDO signals, especially whenenhanced by DNP.

Both schemes B1 and B2 in FIG. 1 rely on a continuous-wave (CW) rf fieldfor ‘sustaining’ or ‘locking’ the LLC, to suppress the chemical shiftsof spins I and S, with a carrier ω_(rf)=(Ω_(I)+Ω_(S))/2 and an rfamplitude that is usually chosen to be larger than the offsetω₁>|Ω_(I)−Ω_(S)|/2. More sophisticated methods may also be used tosustain LLC's over greater bandwidths as described elsewhere.²⁴ Duringrf irradiation, the eigenstates of the Hamiltonian are converted fromthe product base into the singlet-triplet base.⁹ In the process, thedensity operator σ=I_(x)−S_(x) is converted into σ=(|S₀

T₀|+|T₀

S₀|), i.e., into a zero-quantum coherence spanning the central tripletstate T₀=N(|αβ

+βα

) and the singlet state S₀=N(|αβ

−|βα

) where N=2^(−1/2). In the windows τ₃ or τ₃/2, where the rf field isswitched off, the density operator is briefly converted back intosingle-quantum coherences σ=I_(x)−S_(x), so that signals can beobserved. In both schemes B1 and B2 in FIG. 1, the LLC's are sustainedduring the intervals τ2, while the signals are detected in the windowsτ3 or τ₃/2.

The sustain-observe cycles are repeated n times, resulting in ‘sustainedinduction decays’ (SID's) with a total length t^(max)=nΔt digitised atintervals Δt. These Δt intervals are equivalent to the ‘dwell times’ ofordinary free induction decays. The signals can be Fourier transformed,giving a frequency domain spectrum with a digital resolution that isdetermined by 1/t^(max) and a spectral width 1/Δt that should be largerthan the total coupling 2T=2J+4D if one wishes to avoid aliasing.

‘Windowed acquisition’ has been used previously in solid-state NMRmethods such as WAHUHA, MREV and their numerous variants²⁵⁻²⁶ and forhomonuclear dipolar decoupling with shaped rf pulses in the manner ofDUMBO.²⁷ If the observation windows are too short, the signals can beperturbed by transient effects due to transmitter break-through, bearingin mind that the preamplifier must be protected during rf irradiation,and that this protection must be removed in the windows. On the otherhand, if the observation windows are too long, the single-quantumcoherences σ=I_(x)−S_(x) will decay through transverse T₂ relaxation,dephase in the inhomogeneous static field, and evolve under the chemicalshifts and scalar couplings. With an analogue-to-digital converter (ADC)running at 500 kHz, one can acquire a sample point every 2 μs, and takeaverages over all points recorded in each observation interval τ₃ ofscheme B1 or in the first and/or second τ₃/2 interval of scheme B2.Reducing the number of sampling points leads to a loss insignal-to-noise ratio. In practice, the dead time between the pointwhere the CW rf field is switched off and where the signal can beobserved is typically 3 μs, so that 8 sampling points can be taken ineach window if τ₃=20 μs, or 498 points in each window if τ₃=1000 μs. Ifthe sustaining intervals in scheme B1 of FIG. 1 are adjusted to keep aconstant dwell time Δt=τ₂+τ³=50 ms so that a spectral width is 1/Δt=20Hz or ±10 Hz, windows τ₃=20 μs or 1000 μs, lead to rf duty cycles of99.96 or 98% respectively.

During the irradiation intervals τ₂, the coherence Q_(LLC)=(|S₀

T₀|+|T₀

S₀|) evolves under the effect of the total coupling2T_(IS)=2J_(IS)+4D_(IS) and decays with the relaxation rateR_(LLC)=R_(LLC)=1/T_(LLC)

$\begin{matrix}{{\frac{\mathbb{d}}{\mathbb{d}t}Q_{LLC}} = {{- \left( {R_{LLC} + {i\; 2\pi\; T_{IS}}} \right)} \cdot Q_{LLC}}} & (1)\end{matrix}$

In terms of the usual Cartesian product operators, this leads to:σ₂[(I _(x) −S _(x))cos(2πT _(IS)τ2)+(2I _(y) S _(z)−2I _(z) S_(y))sin(2πT _(IS)τ₂)]·exp(−τ₂ ·R _(LLC))  (2)

This is consistent with recent work⁹, but our initial papersunderestimated the effect of the couplings by a factor 2. During eachobservation window τ₃ in the scheme B1 of FIG. 1, the density operatorevolves under the chemical shifts and again under the total couplingconstant T_(IS), albeit reduced by a factor 2, and decays with thesingle-quantum relaxation rate R₂=1/T₂. The overall effect for eachsustain-and-observe cycle Δt=τ₂+τ₃ in scheme B1 can be written:τ₃=cos(ΔΩ_(IS)/2·τ₃)[(I _(x) −S _(x))cos(2πT _(IS) Δt′)+(2I _(y) S_(z)−2I _(z) S _(y))sin(2πT ^(IS) Δt′)]·exp(−<R>Δt)+sin(ΔΩ_(IS)/2·τ₃)[(I_(x) S _(x))cos(2πT _(IS) Δt′)+(2I _(y) S _(z)+2I _(z) S _(y))sin(2πT_(IS) Δt′)]·exp(−<R>Δt)  (3)Where Δt′=τ₂+τ₃/2=Δt−τ₃/2, reflecting the scaling of the total couplingconstant when the rf field is switched off. We can define and apparenttotal coupling constant:T _(IS) ^(app) =T _(IS) Δt′/Δt  (4)

Using the notation R₂=R_(SQC)=κR_(LLC) with κ≦9, the average decay rate<R> in Eq. (3) is

$\begin{matrix}{{< R>={\frac{1}{\Delta\; t}\left( {{\tau_{2}R_{LLC}} + {\tau_{3}R_{2}}} \right)}} = {\frac{\tau_{2} + \tau_{3}}{\tau_{2} + \tau_{3}}R_{LLC}}} & (5)\end{matrix}$

For κ=3, τ₂=49.98 ms and τ₃=20 μs, this amounts to a mere 0.08% increasein the average relaxation rate and hence to a negligible contribution tothe line-width. When the CW rf field along the x-axis is switched onagain, the differences I_(x)−S_(x) and 2I_(y)S_(z)−2I_(z)S_(y) resumetheir identity as LLC's, while the sum I_(x)+S_(x) is spin-locked anddecays, and the sum 2I_(y)S_(z)+2I_(z)S_(y) is dephased under the effectof the rf field inhomogeneity. With a chemical shift differenceΔΩ_(IS)/(2π)=300 Hz, we have cos(ΔΩ_(IS) τ₃)=0.9993˜1. Thisinfinitesimal ‘leakage’ of the LLC may seem negligible, but it isamplified as the sustain-observe sequence is repeated n times withcos(ΔΩ_(IS) τ₃)^(n) so that cos(ΔΩ_(IS) τ₃)¹⁰⁰=0.936, thus affecting thedecay of the LLC. The resulting time domain signals sampled at intervalsΔt are

$\begin{matrix}{{{I\left( {n\;\Delta\; t} \right)} = {I_{0}{{\cos\left( {2\;\pi\; T_{IS}n\;\Delta\; t^{\prime}} \right)} \cdot {\exp\left\lbrack {{- n}\;\Delta\;{t \cdot \left( {{\frac{\tau_{2}}{\tau_{2} + \tau_{3}} \cdot R_{LLC}} + {\frac{\tau_{3}}{\tau_{2} + \tau_{3}} \cdot R_{2}}} \right)}} \right\rbrack}}{\cos\left( {\Delta\;\Omega_{IS}\tau_{3}} \right)}^{n}}}\mspace{20mu}{\ldots = {I_{0}{{\cos\left( {2\;\pi\; T_{IS}^{app}n\;\Delta\; t} \right)} \cdot {\exp\left( {{{- n}\;\Delta\;{t \cdot}} < R >} \right)}}{\cos\left( {\Delta\;\Omega_{IS}\tau_{3}} \right)}^{n}}}} & (6)\end{matrix}$

In order to suppress contributions from I_(x)+S_(x) and2I_(y)S_(z)+2I_(z)S_(y), scheme B2 uses a π pulse in the middle of eachobservation window to refocus the chemical shifts. As a result, thedensity operator at the end of each window τ₃ in scheme B2 is:σ₇=[(I _(x) −S _(x))cos(2πT _(IS) Δt′)+(2I _(y) S _(z)−2I _(z) S_(y))sin(2πT _(IS) Δt′)]·exp(−<R>Δt)  (7)

The resulting time domain signals sampled at intervals Δt are:

$\begin{matrix}{{{{I\left( {n\;\Delta\; t} \right)} = {I_{0}{{\cos\left( {2\;\pi\; T_{IS}n\;\Delta\; t^{\prime}} \right)} \cdot {\exp\left\lbrack {{- n}\;\Delta\;{t \cdot \left( {{\frac{\tau_{2}}{\tau_{2} + {2\tau_{4}}} \cdot R_{LLC}} + {\frac{\tau_{3}}{\tau_{2} + \tau_{3}} \cdot R_{2}}} \right)}} \right\rbrack}}}}\;\mspace{20mu}{\ldots = {I_{0}{{\cos\left( {2\;\pi\; T_{IS}^{app}n\;\Delta\; t} \right)} \cdot {\exp\left( {{{- n}\;\Delta\;{t \cdot}} < R >} \right)}}}}}\mspace{59mu}} & (8)\end{matrix}$Experimental Evidence

FIG. 2 e shows a ‘sustained induction decay’ (SID) that can be comparedwith the FID presented in FIG. 2 a and with the modulated echo decay ofFIG. 2 c. The three signals stem from the two protons in an isotropicsolution (where T_(IS)=J_(IS)) of 2,3-dibromothiophene (20 mM in DMSO-d₆with 30 mM ascorbic acid²⁸ to scavenge paramagnetic oxygen), recordedwith a simple π/2 pulse (FIG. 2 a), observed in a J-resolved 2D manner²⁹(FIG. 2 c), and recorded ‘on the fly’ LLC's in windows τ₃/2=100 isaccording to the invention with scheme B2 (FIG. 2 e). Their Fouriertransforms are presented in FIGS. 2 b, 2 d and 2 f respectively. TheLLC's ‘SID’ signal is described by Eq. (8) and slowly decays with atime-constant <T>=1/<R>=19.9 s. Its Fourier transforms (FIGS. 2 f and 2g) show two lines at ν=±J_(IS) separated by 2J_(IS) with line-widths<Δν>=1/(π<T>)=16.4 mHz (resolution enhanced by a factor ε_(Δ)=ν/<Δν>˜180and 8.5 with respect to conventional FID and echo modulationrespectively). The fact that the couplings are twice as effective in therotating frame than in the laboratory frame is reminiscent of totalcorrelation spectroscopy (‘TOCSY’)³⁰. Note that the antiphase terms2I_(y)S_(z)−2I_(z)S_(y) cannot induce any signals in the orthogonalchannel, so that we have a case of pure amplitude (rather than phase)modulation. The ‘on the fly’ LLC spectrum according to the invention ofthe two diastereotopic protons of glycine in L-Ala-Gly is shown in FIG.2 h.

FIG. 3 a shows how the insertion of refocusing pulses in the middle ofthe observation windows allows one to eliminate the effects of chemicalshifts. For longer windows 100 μs <τ₃<2 ms, scheme B2 provides longerdecays and hence narrower line-widths. Note that the narrowest lines areobtained, albeit at the expense of sensitivity, with scheme B1 with veryshort observation windows (typically τ₃=20 μs). FIG. 3 b shows howrefocusing pulse allow one to obtain an accurate measurement of scalarcouplings J_(IS) (or total couplings T_(IS) in anisotropic media) evenfor long observation windows τ₃. (The slight decrease in J_(IS) ^(app)for long τ₃ is described by Eq. (4)). Finally, FIG. 3 c shows how longerobservation windows τ₃, which allow one to average over a larger numberof data points in each window, result in improved signal-to-noiseratios, which are proportional to τ₃ ^(1/2).

In principle, the evolution of LLC's is immune to the inhomogeneity ofthe magnetic field if one uses the scheme B2 of FIG. 1. We shouldremember however that all excitation schemes A1-A4 of FIG. 1 require oneto distinguish the chemical shifts of the two spins I and S, although itis not necessary to resolve their mutual coupling constant. The methodscan thus tolerate a moderate inhomogeneity of the static field, as longas the line-widths fulfil the condition Δν*=1/(πT₂)*<ΔΩ_(IS).

FIG. 4 shows how a deliberate missetting of the shim currents (z₁, z₂,z₃, x, y, z₀x, and z₀y) to broaden the line-widths in the conventional(single-quantum) spectrum to about Δν*=20 Hz has little effect on theaveraged line-widths <Δν> of the LLC's and the apparent scalar couplingsJ_(IS) ^(app) (+5.3 and +3 mHz, respectively). Ex-situ NMR⁴⁻⁵ and MRI inmoderately inhomogeneous fields (e.g., in the vicinity ofdiscontinuities of the magnetic susceptibility) may benefit from thisproperty.

Very weak molecular alignments, yielding minute residual dipolarcouplings (RDC's) in the mHz range, can be readily determined with theinventive method. FIG. 5 shows the ‘on the fly’ LLC spectra according tothe invention of two solutions of 3-bromothiophene-2-carboxylic acid in(1:1) D₂O/DMSO-d₆, with and without addition of a 0.25% pentaethyleneglycol monododecyl ether (C₁₂E₅). The very weak alignement of the solutegives rise to a net RDC with 2-D_(IS) ^(app)=−10.7±0.4 mHz. The orderparameter of the r_(HH) vector that connects the two protons in3-bromothiophene-2-carboxylic acid can be estimated to be as small asS≦(2.52±0.10)·10⁻⁶ (assuming that the internuclear distance isr_(HH)=2.662 Å like in thiophene³¹, and assuming that the average r_(HH)vector is oriented along B₀, i.e., θ=0).

Since LLC spectra can be recorded in a single scan, they can be boostedby ‘dissolution’ DNP. Spectra of a 20 μL solution of 50 mM2,3-dibromothiophene dissolved in a 3:2 DMSO-d₆/D₂O (v/v) mixture dopedwith 30 mM TEMPOL are compared in FIG. 6 with and withouthyperpolarization by ‘dissolution’ DNP (see Methods section below). Thedissolution, transfer and injection required 3.2 s. After an additional3 s of settling time in the NMR tube, some bubbles and convectioncurrents cannot be ruled out. These tend to broaden ordinary(single-quantum) line-widths, but have little effect on LLC spectra. TheLLC's were excited, sustained, and observed with sequences A3 and B2 ofFIG. 1. The enhancement was ε_(DNP)≈300. It may be possible to improvethis performance by preventing losses of the proton polarization due torelaxation in low fields during the voyage between the DNP polariser andthe NMR magnet.³²

Methods

Sample Preparation

DNP Sample:

a 20 μL solution of 50 mM 3-bromothiophene-2-carboxylic acid (97%,Aldrich) dissolved in a 3:2 mixture of DMSO-d₆/D₂O (v/v) (99.98%,Aldrich) doped with 30 mM 4-Hydroxy-2,2,6,6-tetramethylpiperidine 1-oxyl(TEMPOL) (purum, ≧97.0%, Fluka). The freshly prepared mixture wasrapidly frozen in liquid nitrogen to form 104 beads.

Ascorbate Scavenger:

a 3 M D₂O solution of sodium L-ascorbate (≧99%, Aldrich) was preparedand rapidly frozen in liquid nitrogen (104 beads).

NMR Samples:

a 20 mM isotropic solution of 2,3-dibromothiophene (98% Aldrich) inDMSO-d₆ with addition of 30 mM L-ascorbic acid (BioXtra, ≧99.0%, Sigma)for scavenging paramagnetic oxygen was prepared and sealed in a 5 mm NMRtube.

Aligned Media:

Two 50 mM solution of 3-bromothiophene-2-carboxylic acid in a (1:1)D₂O/DMSO-d₆ mixture with addition of 30 mM L-ascorbic acid forscavenging paramagnetic oxygen were prepared, one with and the otherwithout addition of 0.25% of pentaethylene glycol monododecyl ether(C₁₂E₅, Sigma≧98%) for partial alignment, and sealed in 5 mm NMR tubes.

Peptide Sample:

A 0.5 M solution of L-ala-gly (Sigma) in D₂O with addition of 30 mMsodium L-ascorbate (≧99%, Aldrich) was prepared and sealed in a 5 mm NMRtube. All chemicals were used without further purification.

Hyperpolarization

DNP was performed by thermal mixing at 1.2 K and 3.35 T in a home-built‘dissolution’ DNP polarizer³³⁻³⁵ by applying a CW microwave irradiationat f_(μw)=93.89 GHz and P_(μw)=30 mW for 5 minutes. The DNP build-up of¹H magnetization is fast (τ_(DNP)˜120 s) and yields high proton spinpolarization P(¹H)˜20-40% depending on sample composition.³⁶ About 20 μLof frozen beads of the polarized sample, together with 90 μL of frozenbeads of a 3 M D₂O solution of sodium ascorbate, were rapidly dissolvedwith 3 mL of preheated D₂O (T=440 K and P=1.2 MPa) and intimately mixedwithin 700 ms, transferred in 1.5 s to a 11.7 T NMR magnet through a 1mm inner diameter PTFE tube pressurized with helium gas at 0.6 MPa, andallowed to settle for 0.5 s, prior to injection into a pre-locked NMRtube, which required another 0.5 s. After a further 3 s settling time inthe NMR tube to allow turbulences to slow down, the LLC was excited,sustained, and observed with the sequences A3 and B2 of FIG. 1.

NMR Measurements

NMR measurements were performed on a 500 MHz spectrometer equipped withan Inverse 5 mm Bruker CryoProbe™. The ‘on the fly’ LLC pulse programand excitation/acquisition sequences were designed and performed withTopSpin 2.1.

In conclusion, the present invention describes an ‘on-the-fly’ methodwhere the radio-frequency (rf) irradiation required to sustain the LLC'sin high magnetic field is briefly interrupted, normally at regularintervals, so that the LLC's are temporarily converted intosingle-quantum coherences (SQC's) that can be observed. The methodaccording to the invention allows one to obtain ultra high-resolutionspectra of long-lived coherences (LLC's) ‘on the fly’ in one-dimensionalfashion by time-shared ‘windowed acquisition’. This allows one todetermine very accurate total couplings T=J+2D. The method can beapplied to either isotropic or anisotropic phases, providing ultra-highresolution even in moderately inhomogeneous magnetic fields. The signalscan be enhanced by “dissolution” DNP¹⁰. The technique has been appliedto pairs of spins in this study, but it is intended to extend the scopeof application of ‘on the fly’ LLC's in the near future to multiple spinsystems (N>2) with broad-band excitation and detection (replacing CW bycomposite pulses) of several LLC's in the same molecule or in mixtures.Since inhomogeneous fields are not detrimental to LLC's, ex-situ orin-cell studies should be readily feasible with unprecedentedlinewidths, and since the long lifetimes of LLC's are exquisitelysensitive to the presence of paramagnetic species²⁸, we believe theyshould be sensitive probes for the detection paramagnetic species suchas oxygen.

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We claim:
 1. A method for nuclear magnetic resonance (NMR) spectroscopyof a sample, the method comprising the steps of: a) exciting long livedcoherences (LLC) between a singlet state S₀ and a central triplet stateT₀ of nuclei of the sample by irradiating the sample with an rf-fieldhaving a carrier frequency ω_(rf); b) sustaining the LLC by maintainingrf-irradiation during an interval τ₂; c) temporarily converting the LLCinto observable magnetisation by interrupting the rf-irradiation duringan observation interval τ₃; d) detecting NMR-signals during theobservation interval τ₃; e) reconverting the observable magnetisationback into LLC after the observation interval τ₃; and f) repeating steps(b) to (e) n times, wherein n is a positive integer.
 2. The method ofclaim 1, comprising exciting the LLC by transforming an initial spinpolarization, (I_(z)+S_(z)) into single quantum coherences (I_(x)−S_(x))or (I_(y)−S_(y)) or (2I_(y)S_(x)−2I_(z)S_(y)) or (2I_(x)S_(z)−2IS_(x))prior to initiating irradiation of the sample with the rf-field.
 3. Themethod of claim 2, wherein the initial spin polarization is a thermalequilibrium Boltzmann distribution.
 4. The method of claim 1, comprisinghyperpolarizing the sample to enhance a spin polarization (I_(z)+S_(z)),thereby enhancing LLC that are subsequently excited by transforming theenhanced spin polarization (I_(z)+S_(z)) into enhanced single quantumcoherences (I_(x)−S_(x)) or (I_(y)−S_(y)) or (2I_(y)S_(z)−2I_(z)S_(y))or (2I_(x)S_(z)−2I_(z)S_(x)) prior to initiating irradiation of thesample with the rf-field.
 5. The method of claim 4, comprisinghyperpolarizing the sample using dynamic nuclear polarization.
 6. Themethod of claim 1, wherein the carrier frequency isω_(rf)=(Ω_(I)−Ω_(S))/2, wherein Ω_(I) is a chemical shift of nuclei ofthe sample with spin I, and wherein Ω_(S) is a chemical shift of nucleiof the sample with spin S.
 7. The method of claim 1, wherein therf-field is a continuous-wave rf-field.
 8. The method of claim 1,wherein the rf-field is modulated in amplitude.
 9. The method of claim1, wherein the rf-field is modulated in phase.
 10. The method of claim6, wherein an amplitude of the rf-field is larger than an offset|Ω_(I)−Ω_(S)|/2.
 11. The method of claim 1, comprising applying arefocusing pulse in a middle of the observation interval τ₃.
 12. Themethod of claim 1, comprising carrying out an NMR spectroscopymeasurement in a single experiment.